The Higgs gateway to new physics: first steps into terra incognita

In this talk, I will present exciting phenomenological opportunities involving the Higgs boson in the quest for new physics. I will focus on three examples. First, I will highlight the relevance of the Higgs couplings at high energy scales through the off-shell Higgs measurement. Then, I will present some prospects to directly probe CP-violation in the Higgs sector at the LHC. Finally, I will discuss some paths towards precision using the HL-LHC data.